Chapter 23, Problem 99PP

Loop Detectors on Roadways

“Smart” traffic lights are controlled by loops of wire embedded in the road (Figure 23). These “loop detectors” sense the change in magnetic field as a large metal object—such as a car or a truck—moves over the loop. Once the object is detected, electric circuits in the controller check for cross traffic, and then turn the light from red to green.

A typical loop detector consists of three or four loops of 14-gauge wire buried 3 in. below the pavement. You can see the marks on the road where the pavement has been cut to allow for installation of the wires. There may be more than one loop detector at a given intersection; this allows the system to recognize that an object is moving as it activates first one detector and then another over a short period of time. If the system determines that a car has entered the intersection while the light is red, It can activate one camera to take a picture of the car from the front—to see the driver’s face—and then a second camera to take a picture of the car and its license plate from behind This red-light camera system was used to good effect during an exciting chase scene through the streets of London in the movie National Treasure Book of Secrets.

Motorcycles are small enough that they often fail to activate the detectors, leaving the cyclist waiting and waiting for a green light. Some companies have begun selling powerful neodymium magnets to mount on the bottom of a motorcycle to ensure that they are “seen” by the detectors.

•• Suppose a motorcycle increases the downward component of the magnetic field within a loop only from 1.2 × 10⁻⁵ T to 1.9 × 10⁻⁵ T. The detector is square, is 0.75 m on a side, and has four loops of wire. Over what period of time must the magnetic field increase if it is to induce an emf of 14 × 10⁻⁴ V?

1. A.    0.028 s
2. B.     0.11s
3. C.     0.35 s
4. D.    0.60 s